Manmohan Singh cautioned that while PM Modi spoke about the dedication to national unity, it must not be jeopardised by "authoritarian hubris."
Earlier this month, Nitish Kumar had split from the BJP and established a coalition government with the RJD and other parties, including the Congress.
Atal Bihari Vajpayee had previously held the position of prime minister of India three times—briefly in 1996, between 1998 and 1999, and again for a full term from 1999 to 2004.